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Comment by sokoloff | Hacker News Reader

DCA makes mathematical sense anytime you have a long-term bullish thesis (otherwise, "do not invest" is a better strategy), but have a belief that there is a short-term noise function super-imposed over the long-term uptrend and where that short-term noise function is relatively large in amplitude as compared to the expected long-term growth over the period.

DCA makes psychological sense if the concern is a FOMO on the best possible entry price. It takes the psychological pressure of finding the absolute best off the table and replaces it with a smoothed average entry price.

I think it's a more powerful psychological device (and I do tend to invest pretty much all at once when I reach a decision), but it's not entirely pointless mathematically.

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> DCA makes mathematical sense anytime you have a long-term bullish thesis (otherwise, "do not invest" is a better strategy), but have a belief that there is a short-term noise function...

Math citation needed - the noise function you're hypothesizing could just as easily drive the average up as down, unless you have a reason to think it should go down, in which case you're timing the market and there's a better future time to go 100%.

Of course it could just as easily drive the average up, but the point is that it's a hedge: it's accepting a reduced chance of possible higher returns for the safety of reduced chance of possible lower returns.

But it's not a hedge.

If you commit to the strategy (buy monthly for 10 months) then you're just choosing an unknown price over a known price.

And if you don't commit to the strategy, then you're actively trading and not DCA'ing.

Isn't it still a hedge? Statistically, you'll get the average price of the stock for the period you DCA. While if you enter at any single moment, you get a somewhat random price.

Another thought: if the thesis is that the price will go up, then whatever sum you have and want to invest, should you invest it all now - given that the price is supposed to go up?

If you commit to the strategy in advance, then you're picking an unknown price instead of a current price, and the unknown price is likely higher.

A financial hedge is, generally, something which reduces risk or improves on the risk:reward ratio in a mathematically demonstrable way. Generally this means bundling uncorrelated (or anticorrelated) assets. This concept won a Nobel for Econ in 1990(?), and is the foundation of modern portfolio theory.

Using "hedge" in a more colloquial way, it can mean "a way to protect yourself from an unexpected poor outcome". But by that definition this also fails, since you're just as vulnerable to outlier events, but the nature of those outlier events is different (and perhaps less intuitive).

This makes sense, thanks!

I believe you're right, but I have always thought DCA was just a measure to transform "fixed amount to savings account" people into "fixed amount to Vanguard" people so that they can access the higher risk that is the S&P500 compared to a savings bank account.

You can simplify the mathematical argument a lot by looking at DCA as forcing a relative "buy low sell high." When the price of the asset is lower, your DCA buys more, when it's higher you buy less. Relative to a single purchase at the average price, this is equivalent to buying low and selling high.

A single purchase at the weighted average price is the same as the DCA'd purchase. In both cases you buy X shares for Y$.

Imagine you commit to buying $100 on each of date A, B, and C. On A, the price is $10/share. You buy 10 shares. On B, it’s $100/sh. You buy 1 share. On C, it’s $1/sh. You buy 100 shares. You have 111 shares at a cost-basis of $300 (or $2.70/share).

The time-weighted average price was $37/share.

DCA is a way to force yourself to make purchases at a variety of prices and times. (How likely is it with a single-purchase strategy that you'd own 111 shares at $2.70/sh of a stock that charted $10->$100->$1? How would you feel when you saw your $300 investment go to $111 in value? DCA takes a lot of that psychological pressure off and is amenable to decide-once and automate.)

> DCA takes a lot of that psychological pressure off...

Yes, that exactly. It's a psychological trick (if you have all the money upfront) and not a financially sound one.

Interesting…. Under what assumptions precisely is it optimal to dollar cost average over a short time interval, if short time fluctuations have a large magnitude relative to long term drift? Like eg if you assume geometric brownian motion it doesn’t seem to help?

Yes, you're correct about geometric brownian motion. The model must include some mean-reverting component (implied by "short time fluctuations") for DCA to come out ahead, and such a component would violate standard no-arbitrage assumptions.

This is a reason I haven't made active use of DCA. But DCA doesn't give up much, either, so I'm fine with "passively" engaging in DCA-like behavior by haphazardly dumping spare money into index funds after min("significant" drop, time limit) instead of purely maximizing time in market.

In principal, how do I pick whether to DCA over 10 years, 1 year, 1 month, 1 day, or 1 hour?

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